Problem: Find the greatest common factor of $30$ and $18$.
Solution: The greatest common factor (GCF) is the largest number that is a factor of both $30$ and $18$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}30 &=2\cdot3\cdot5\\\\\\\\ 18&=2\cdot3\cdot3 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}30 &=2\cdot3\cdot5\\\\\\\\ 18&=2\cdot3\cdot3 \end{aligned}$ Each number shares the factors ${2}$ and ${3}$, so the GCF is $2\cdot3=6$. The greatest common factor of $30$ and $18$ is $6$.